Download or read book Matrix Based Multigrid written by Yair Shapira and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many important problems in applied science and engineering, such as the Navier Stokes equations in fluid dynamics, the primitive equations in global climate mod eling, the strain-stress equations in mechanics, the neutron diffusion equations in nuclear engineering, and MRIICT medical simulations, involve complicated sys tems of nonlinear partial differential equations. When discretized, such problems produce extremely large, nonlinear systems of equations, whose numerical solution is prohibitively costly in terms of time and storage. High-performance (parallel) computers and efficient (parallelizable) algorithms are clearly necessary. Three classical approaches to the solution of such systems are: Newton's method, Preconditioned Conjugate Gradients (and related Krylov-space acceleration tech niques), and multigrid methods. The first two approaches require the solution of large sparse linear systems at every iteration, which are themselves often solved by multigrid methods. Developing robust and efficient multigrid algorithms is thus of great importance. The original multigrid algorithm was developed for the Poisson equation in a square, discretized by finite differences on a uniform grid. For this model problem, multigrid exhibits extremely rapid convergence, and actually solves the problem in the minimal possible time. The original algorithm uses rediscretization of the partial differential equation (POE) on each grid in the hierarchy of coarse grids that are used. However, this approach would not work for more complicated problems, such as problems on complicated domains and nonuniform grids, problems with variable coefficients, and non symmetric and indefinite equations. In these cases, matrix-based multi grid methods are in order.
Download or read book Multigrid Methods written by Ulrich Trottenberg and published by Academic Press. This book was released on 2001 with total page 652 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Computing -- Numerical Analysis.
Download or read book A Multigrid Tutorial written by William L. Briggs and published by SIAM. This book was released on 2000-07-01 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Computing -- Numerical Analysis.
Download or read book Numerical Solution of Partial Differential Equations on Parallel Computers written by Are Magnus Bruaset and published by Springer Science & Business Media. This book was released on 2006-03-05 with total page 491 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the dawn of computing, the quest for a better understanding of Nature has been a driving force for technological development. Groundbreaking achievements by great scientists have paved the way from the abacus to the supercomputing power of today. When trying to replicate Nature in the computer’s silicon test tube, there is need for precise and computable process descriptions. The scienti?c ?elds of Ma- ematics and Physics provide a powerful vehicle for such descriptions in terms of Partial Differential Equations (PDEs). Formulated as such equations, physical laws can become subject to computational and analytical studies. In the computational setting, the equations can be discreti ed for ef?cient solution on a computer, leading to valuable tools for simulation of natural and man-made processes. Numerical so- tion of PDE-based mathematical models has been an important research topic over centuries, and will remain so for centuries to come. In the context of computer-based simulations, the quality of the computed results is directly connected to the model’s complexity and the number of data points used for the computations. Therefore, computational scientists tend to ?ll even the largest and most powerful computers they can get access to, either by increasing the si e of the data sets, or by introducing new model terms that make the simulations more realistic, or a combination of both. Today, many important simulation problems can not be solved by one single computer, but calls for parallel computing.
Download or read book Matrix Computations written by Gene H. Golub and published by JHU Press. This book was released on 2013-02-15 with total page 781 pages. Available in PDF, EPUB and Kindle. Book excerpt: This revised edition provides the mathematical background and algorithmic skills required for the production of numerical software. It includes rewritten and clarified proofs and derivations, as well as new topics such as Arnoldi iteration, and domain decomposition methods.
Download or read book Multilevel Block Factorization Preconditioners written by Panayot S. Vassilevski and published by Springer Science & Business Media. This book was released on 2008-10-22 with total page 527 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is the first to provide a comprehensive, self-contained and rigorous presentation of some of the most powerful preconditioning methods for solving finite element equations in a common block-matrix factorization framework. The book covers both algorithms and analysis using a common block-matrix factorization approach which emphasizes its unique feature. Topics covered include the classical incomplete block-factorization preconditioners, the most efficient methods such as the multigrid, algebraic multigrid, and domain decomposition. This text can serve as an indispensable reference for researchers, graduate students, and practitioners. It can also be used as a supplementary text for a topics course in preconditioning and/or multigrid methods at the graduate level.
Download or read book Multigrid Methods written by Stephen F. McCormick and published by SIAM. This book was released on 1987-12-01 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: A thoughtful consideration of the current level of development of multigrid methods, this volume is a carefully edited collection of papers that addresses its topic on several levels. The first three chapters orient the reader who is familiar with standard numerical techniques to multigrid methods, first by discussing multigrid in the context of standard techniques, second by detailing the mechanics of use of the method, and third by applying the basic method to some current problems in fluid dynamics. The fourth chapter provides a unified development, complete with theory, of algebraic multigrid (AMG), which is a linear equation solver based on multigrid principles. The last chapter is an ambitious development of a very general theory of multigrid methods for variationally posed problems. Included as an appendix is the latest edition of the Multigrid Bibliography, an attempted compilation of all existing research publications on multigrid.
Download or read book Facing the Multicore Challenge II written by Rainer Keller and published by Springer. This book was released on 2012-05-13 with total page 181 pages. Available in PDF, EPUB and Kindle. Book excerpt: This state-of-the-art survey features topics related to the impact of multicore, manycore, and coprocessor technologies in science and for large-scale applications in an interdisciplinary environment. The papers cover issues of current research in mathematical modeling, design of parallel algorithms, aspects of microprocessor architecture, parallel programming languages, hardware-aware computing, heterogeneous platforms, manycore technologies, performance tuning, and requirements for large-scale applications. The contributions presented in this volume offer a survey on the state of the art, the concepts and perspectives for future developments. They are an outcome of an inspiring conference conceived and organized by the editors at the Karlsruhe Institute Technology (KIT) in September 2011. The twelve revised full papers presented together with two contributed papers focus on combination of new aspects of microprocessor technologies, parallel applications, numerical simulation, and software development; thus they clearly show the potential of emerging technologies in the area of multicore and manycore processors that are paving the way towards personal supercomputing and very likely towards exascale computing.
Download or read book Multigrid Methods V written by Wolfgang Hackbusch and published by Springer. This book was released on 1998-10-20 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a selection from the papers presented at the Fifth European Multigrid Conference, held in Stuttgart, October 1996. All contributions were carefully refereed. The conference was organized by the Institute for Computer Applications (ICA) of the University of Stuttgart, in cooperation with the GAMM Committee for Scientific Computing, SFB 359 and 404 and the reserach network WiR Ba-Wü. The list of topics contained lectures on Multigrid Methods: robustness, adaptivity, wavelets, parallelization, application in computational fluid dynamics, porous media flow, optimisation and computational mechanics. A considerable part of the talks focused on algebraic multigrid methods.
Download or read book Algebraic Multigrid for the Multi ion Transport and Reaction Model written by Peter Thum and published by Logos Verlag Berlin GmbH. This book was released on 2012 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: Das Multi-Ionen Transport und Reaktionsmodell wird fur die Simulation von elektrochemischen Prozessen eingesetzt. Das durch das Modell gegebene System partieller Differentialgleichungen (PDE) wird mit Hilfe einer gemischten Residuen-Distribution und Finiten Elemente Methode diskretisiert und mit dem Newton Verfahren linearisiert. Dabei entstehen eine Reihe linearer Gleichungssyteme.Die Dissertation beschreibt ein physikalisch orientiertes algebraisches Mehrgitterverfahren, welches zur effizienten und robusten Losung dieser linearen Gleichungssyteme eingesetzt werden kann. Insbesondere wird auf die Reihenfolge der Variablen und deren Wirkung auf das Glattungsverhalten eingegangen. Bei der Konstruktion der Grobgitterkorrektur werden Aspekte wie eine verletzte Peclet Bedingung und die Nichtlinearitat des PDE Systems beachtet.
Download or read book Iterative Methods for Sparse Linear Systems written by Yousef Saad and published by SIAM. This book was released on 2003-04-01 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Computing -- General.
Download or read book 100 Volumes of Notes on Numerical Fluid Mechanics written by Ernst Heinrich Hirschel and published by Springer Science & Business Media. This book was released on 2009-05-19 with total page 507 pages. Available in PDF, EPUB and Kindle. Book excerpt: In a book that will be required reading for engineers, physicists, and computer scientists, the editors have collated a number of articles on fluid mechanics, written by some of the world’s leading researchers and practitioners in this important subject area.
Download or read book Multigrid Techniques written by Achi Brandt and published by SIAM. This book was released on 2011-01-01 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt: This classic text presents the best practices of developing multigrid solvers for large-scale computational problems in science and engineering. By representing a problem at multiple scales and employing suitable interscale interactions, multigrid avoids slowdown due to stiffness and reduces the computational cost of classical algorithms by orders of magnitude. Starting from simple examples, this book guides the reader through practical stages for developing reliable multigrid solvers, methodically supported by accurate performance predictors. The revised edition presents discretization and fast solution of linear and nonlinear partial differential systems; treatment of boundary conditions, global constraints and singularities; grid adaptation, high-order approximations, and system design optimization; applications to fluid dynamics, from simple models to advanced systems; new quantitative performance predictors, a MATLAB sample code, and more. Readers will also gain access to the Multigrid Guide 2.0 Web site, where updates and new developments will be continually posted, including a chapter on Algebraic Multigrid.
Download or read book Scientific Computing in Electrical Engineering written by Andreas Bartel and published by Springer. This book was released on 2016-05-09 with total page 251 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of selected papers presented at the 10th International Conference on Scientific Computing in Electrical Engineering (SCEE), held in Wuppertal, Germany in 2014. The book is divided into five parts, reflecting the main directions of SCEE 2014: 1. Device Modeling, Electric Circuits and Simulation, 2. Computational Electromagnetics, 3. Coupled Problems, 4. Model Order Reduction, and 5. Uncertainty Quantification. Each part starts with a general introduction followed by the actual papers. The aim of the SCEE 2014 conference was to bring together scientists from academia and industry, mathematicians, electrical engineers, computer scientists, and physicists, with the goal of fostering intensive discussions on industrially relevant mathematical problems, with an emphasis on the modeling and numerical simulation of electronic circuits and devices, electromagnetic fields, and coupled problems. The methodological focus was on model order reduction and uncertainty quantification. this book="" will="" appeal="" to="" mathematicians="" and="" electrical="" engineers.="" it="" offers="" a="" valuable="" starting="" point="" for="" developers="" of="" algorithms="" programs="" who="" want="" learn="" about="" recent="" advances="" in="" other="" fields="" as="" well="" open="" problems="" coming="" from="" industry.="" moreover,="" be="" use="" representatives="" industry="" with="" an="" interest="" new="" program="" tools="" mathematical="" methods.
Download or read book Challenges in Scientific Computing CISC 2002 written by Eberhard Baensch and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: The conference Challenges In Scientific Computing (CISC 2002) took place from October, 2 to 5, 2002. The hosting institution was the Weierstrass Insti tute for Applied Analysis and Stochastics (WIAS) in Berlin, Germany. The main purpose of this meeting was to draw together researchers working in the fields of numerical analysis and scientific computing with a common interest in the numerical treatment and the computational solution of systems of nonlinear partial differential equations arising from applications of physical and engineering problems. The main focus of the conference was on the problem class of non linear transport/diffusion/reaction systems, chief amongst these being: the Navier-Stokes equations, semiconductor-device equations and porous media flow problems. The emphasis was on unsolved problems, challenging open questions from applications and assessing the various numerical methods used to handle them, rather than concentrate on accurate results from "solved" problems. Thanks to the participants it was an interesting meeting. The presentations stimulated exchanging ideas and lively discussions. This proceedings comprises 13 papers form the conference, ranging from numerical methods for flow problems, multigrid methods, semiconductor and microwave simulation, solution methods, finite element analysis to software aspects. This interesting conference would not have been possible without the help of the staff of the WIAS. I thank all participants, and all our supporters, especially those not onstage, for making the conference a success.
Download or read book Image Processing Based on Partial Differential Equations written by Xue-Cheng Tai and published by Springer Science & Business Media. This book was released on 2006-11-22 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book publishes a collection of original scientific research articles that address the state-of-art in using partial differential equations for image and signal processing. Coverage includes: level set methods for image segmentation and construction, denoising techniques, digital image inpainting, image dejittering, image registration, and fast numerical algorithms for solving these problems.
Download or read book An Introduction to Multigrid Methods written by Pieter Wesseling and published by R.T. Edwards, Inc.. This book was released on 2004 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduces the principles, techniques, applications and literature of multigrid methods. Aimed at an audience with non-mathematical but computing-intensive disciplines and basic knowledge of analysis, partial differential equations and numerical mathematics, it is packed with helpful exercises, examples and illustrations.
